The 2SLS output provides the F-Statistic, is this the same as the first-stage f-statistic reported in Stata? They are providing different results, should this be the case? If so, can someone explain why? Thanks

The EViews 2SLS output produces the F-statistic for the significance of the regressors in the 2SLS specification, not for the first-stage. Bearing in mind that I am not certain what Stata is doing, if they are producing an F-statistic based on the first stage, it would presumably be quite different.

I just noticed that Startz posted a reply to your original question. Coincidentally, I was going to provide you with a reference:

I'm not certain of which Wooldridge reference you are citing, nor his recommeded workarounds. The R2 form of F-statistics is an computational shortcut that one can use in certain, but not all, cases. EViews has never used this shortcut; the reference I provided above describes in great detail what we do.